incumbents' interests and gender quotas

Incumbents’ Interests and Gender Quotas

Guillaume R. Frechette New York UniversityFrancois Maniquet C.O.R.E.Massimo Morelli Columbia University

The introduction of mandatory gender quotas in party lists is a reform that many countries have recently adopted orhave been considering. The electoral system affects the incumbents’ incentives to make such reforms, their details, andtheir effectiveness. We show that male incumbents can actually expect an increased incumbency advantage when genderquotas are introduced, if they are elected through single-member district majority rule. On the other hand, no expectationof male advantage can reduce the incumbents’ fear of being replaced if they are elected through closed-list proportionalrepresentation. As France has both electoral systems, we validate the above argument using a formal model of constitutionaldesign as well as an empirical analysis of the legislative elections in France, displaying the existence of male bias in thelast three elections. We also show that parity may have Assembly composition effects and policy effects that vary with theelectoral system.

In June 2000, the French National Assembly, in spiteof the opposition of the Senate, passed a law—the so-called “parity law”—that requires parties to choose

roughly equal numbers of men and women as candidatesin their lists. Such a parity law is the only case of stronggender quotas for chambers using single-member districtelections.1 However, the law also prescribes that partiesfailing to present an equal number of men and women

Guillaume R. Frechette is assistant professor of economics, New York University, 19 West Fourth Street, 6th Floor, New York, NY 10012-9873([email protected]). Francois Maniquet is professor of economics, Center for Operations Research and Econometrics (CORE), UniversiteCatholique de Louvain, Louvain-la-Neuve, Belgium ([email protected]). Massimo Morelli is professor of political scienceand economics, Columbia University, 720 LAB, 420 W. 118th St., New York, NY 10027 ([email protected]).

We are highly indebted to Joan Scott for inspiring us and for many discussions on the parity movement in France. We are grateful tothe Institute for Advanced Study in Princeton for giving us the opportunity to start this project. Comments by Matt Jackson, DeanLacy, Matthias Messner, Kira Sanbonmatsu, Gilles Serra, Ken Shepsle, Guido Tabellini, Jack Wright, four anonymous referees, and by theparticipants at various workshops are gratefully acknowledged. We thank Ji Li, Chloe Tergiman, and Violette Van Dyck for their assistancewith the data as well as the Centre de Donnees Socio-Politiques for providing us with some of the data. Morelli gratefully acknowledgesthe financial support of the National Science Foundation (Grants SES-0213312 and SES-0519045) and the Deutsche Bank. Maniquetthanks the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science PolicyProgramming. Frechette’s research was partially supported by the Center for Experimental Social Science, the C.V. Starr Center, and theNational Science Foundation (Grants SES-0519045 and SES-0721111). Any opinions, findings, and conclusions or recommendations inthis material are those of the authors and do not necessarily reflect the views of the institutions supporting the project.

1The French Assembly is formed using single-member district majority rule. The Senate is elected using plurality rule in small districts andclosed-list proportional representation in large ones. The two chambers are called by the Constitution to vote together on constitutionalreforms like the one discussed here. Since the Assembly has the last word (see footnote 34 for more details), explaining the almostunanimous support of the reform in the Assembly, is sufficient to understand the approval of the reform. The parity law takes differentforms in the different types of elections, and in the case of the Assembly, it means that each party should have between 48% and 52% ofcandidates of each gender across districts. For closed-list elections, the parity law requires the parties to alternate men and women in thelists.

2Norwegian parties were the first ones to introduce such quotas, which are now widespread in Northern Europe and elsewhere.

3Lower than 50% legal quotas have been introduced, for example, in Argentina, Costa Rica, and Belgium.

4A summary of the legislations and effects of gender quotas across countries and electoral systems can be found in Table 1 of Jones (2004).

on their lists will not be eliminated from the competitionbut will pay per-violation fines.

In the first legislative elections that followed, in 2002,the fraction of female candidates elected for the Assem-bly surprisingly stayed almost constant (12.3% insteadof 10.9%), well below that in countries where quotas arevoluntarily introduced by parties2 or where legal quo-tas are lower.3,4 What can motivate the members of a

American Journal of Political Science, Vol. 52, No. 4, October 2008, Pp. 891–907

C©2008, Midwest Political Science Association ISSN 0092-5853

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892 GUILLAUME R. FRECHETTE, FRANCOIS MANIQUET, AND MASSIMO MORELLI

male-dominated Parliament to make such a strong kind ofgender representation reform? Why were deputies almostunanimously in favor of the reform while the Senatorswere mostly opposed? Why was the law so unsuccessfulat achieving its purported aim of gender equity at theAssembly level (whereas it was much more successful,for instance, at the municipal level)? This article aims toprovide a consistent set of answers to these questions, bymeans of a simple formal model of constitutional reformincentives as well as empirical analysis.

Our explanation relates to the special incentivescreated by the Assembly electoral system (SMD) whendeputies expect their incumbency advantage to riseagainst the new challengers imposed by the reform.5 Be-cause of the increased incumbency advantage induced bythe parity law in a male-dominated status quo, it shouldbe clear why incumbent deputies were unanimously infavor of the reform.

By proving that the self-interest of a majority can suf-fice to explain the introduction of laws that prima facieprotect or foster minority interests,6 and by insisting onthe role of the electoral system in creating such incen-tives, we introduce a new look at demand and supply sideexplanations of affirmative action policies. This articlealso opens a new door in the analysis of the relationshipbetween electoral systems and women representation. Ithas, of course, long been observed that electoral ruleshave a huge impact on the fraction of women elected(see Duverger 1955). There is a long literature on thistopic, trying in particular to explain why the fraction offemale legislators is larger and increases more rapidly un-der Proportional Representation than under SMD (see,e.g., Matland and Studlar 1996; Rosenthal 1995; Siaroff2000). A common feature of that literature is that theelectoral rules are viewed as exogenous variables. That

5As it will be clear from the analysis, the male incumbents as well asnew male candidates had significant advantage over similar femaleincumbents or new candidates in the last three legislative electionsin France. The advantage for male incumbents is the one we referto when saying that it was to be expected, since the dominant roleof male politicians within party organizations prior to the reform(documented, for instance, in Appleton and Mazur 1994) meantthat most of the new female candidates determined by the intro-duction of parity law would have to be much less experienced andestablished than the challenger the incumbent would have had toface without the reform. We will then see in the analysis that themale advantage proved to be more widespread than this under-standable one for incumbents, and it will be possible to analyzewhether this advantage may have been determined also by voters’bias, but the existence of explicit gender bias among voters is notessential for the constitutional reform incentives argument.

6Our theoretical and empirical analyses relate to the incumbents’interests vis-a-vis legal candidacy quotas. The analysis of the incen-tives of party members to pass voluntary quotas at the individualparty level is beyond the scope of this article.

is, the possibility that identical factors determine boththe electoral rules and the representation of women (orthe effectiveness of some affirmative action policies) isignored. Our contribution precisely consists of showingthat electoral rules (in our case, the parity law) and the re-sulting low number of women elected are both explainedby the same factors.

Given the importance of the male advantage assump-tion for the main theoretical point of the article, our com-plementary empirical analysis will be devoted to carefullyestablishing the existence of a male advantage in the datafrom all the most recent French elections.7 In the nextsection we present the model with which we prove thatthe existence of male advantage gives male incumbentsthe incentive, under an SMD electoral system, to pass aparity law of exactly the form we observe in France. In thefourth section, we concentrate on the opposition to thelaw by Senators, linking it again to the electoral system.The Senate, indeed, uses a PR system (in sufficiently largedistricts), and parity requires placing women in alternat-ing positions on the party list. While such a system shouldeventually achieve gender equality (hence the oppositionof male incumbent Senators), we will show how the vot-ers’ very low willingness to punish parties circumventingthe law was strategically exploited by male incumbentSenators to maintain their seat. In the last section, weoffer some concluding comments.

In the remainder of the introduction, we would like(1) to present in greater detail our theory and its empiricalfoundations, (2) to argue why alternative explanationsfind less support in the data, and finally, (3) to discussthe possible reconciliation between this article and theexisting literature.

Let us first give more details about the theory. Our for-mal model suggests that passing parity with the provisionof possible fees dominates all other options (namely thestatus quo and pure parity without violations allowed) ifthe reelection of incumbents matters more to party lead-ers than the election of new candidates. The argumentgoes as follows: given voters’ bias in favor of men can-didates or any other source of male advantage due, forinstance, to expected party bias and party history, par-ties are in favor of a gender quota because it increasesthe incumbents’ probability (conditional on running) ofrunning against a woman and being reelected. On theother hand, pure parity (with no violations allowed)

7To be precise, the “male advantage” empirical finding shown in thesecond section is that, controlling for observables, when a new (orincumbent) male candidate runs against a woman, he does betterthan male and female new (or incumbent) candidates runningagainst an opponent of the same sex. Similarly, females runningagainst males do worse than females running against females.

INCUMBENTS’ INTERESTS AND GENDER QUOTAS 893

decreases the probability for the male incumbents of alarge party to run again. Therefore, fees are rationalizableas they constitute a direct way to make more incumbentsrun than the strict application of parity would allow. Theex ante drawback of parity with fees is that if one partypays fees, this obviously decreases the other party’s in-cumbents’ chances of running against a woman.

Therefore, it is not always true that parity with feesex ante dominates both strict parity and no-parity. Weprove in the third section that there exist values of thefees and the preference by party leaders for incumbentsover new candidates that guarantee that, in equilibrium,parties are willing to pay fees only in order to allow incum-bents to run. Parity with fees, then, has the two attractiveproperties (for the incumbents) that (1) it increases theprobability for incumbents to run against women, and (2)it does not prevent incumbents from large parties fromrunning. Finally, the presence of male advantage and theaccess to (costly) violations of the quota also explain whythe percentage of women elected did not increase verymuch in the two Assembly elections that occurred afterthe introduction of parity.

Coming to the relationship between our account ofparity and alternative potential explanations, our firstcaveat is that we do not claim to have a complete story forthe adoption of the law. For instance, we completely dis-regard the surely essential role of feminist movements.8

French feminists and other progressive movements in theyears before the parity law were certainly a factor forcingthe members of Parliament to take the issue seriously, andsuch pressure may well belong to the list of explanatoryvariables for the timing of the reform.9 However, a theoryonly based on lobbying and social movements does notexplain why the French deputies supported almost unani-mously a parity law at a time in which the French Senatorsalmost unanimously objected it and no other EuropeanParliament was ready to approve even lower quotas, inthe presence of similar pressures by similar movements.

8Greater feminist activism has been shown to affect women repre-sentation (see, e.g., Caul 1999).

9Any attempt to explain the timing of the reform should take intoaccount the pressure by the parity movements as well as the particu-lar incentive structure for incumbents identified here for Assemblydeputies. An example about how these two elements may have beencomplementary in the explanation of the reform is the following:the parity movement had an impact also through internal pressureswithin the socialist party, which was expecting to lose support; in-troducing parity was perhaps viewed by the socialist party leadersas a way to introduce a topic that ceteris paribus was expected tobe in their favor and that would also temporarily raise incumbencyadvantage to maintain their seat; the others voted for it becauseas incumbents they were not going to be affected for a while, andgoing against it would have been unpopular and would have madethe issue more salient.

The most common explanation of the French passingof the law followed by its low success (explanation de-fended by the official “Observatoire de la parite entre lesfemmes et les hommes” in their report to the Prime Min-ister following the elections, see Zimmerman 2003 andby scientists, see for instance Sineau 2002) is the follow-ing one: deputies passed a parity law because the Frenchpeople wanted it, that is, parity was a symbolic gesture as-sociated with a demand of parity from the electorate, butit was rather ineffective because of the power of incum-bents to force the party to circumvent the law (by payingfees) and be able to run. There are three logical difficultiesor shortcomings associated with this explanation. First, ifdeputies passed the law to meet the will of the people, whywere the Senators so forcefully against it? We describe atlength how the Senators tried to amend the law and howthe electoral system changed in the subsequent years todecrease its impact. We also explain why the impact ofparity has been so limited in spite of the theoretically fa-vorable electoral system. We view that as a clear proof thatSenators tried to defend their seats, which the parity lawthreatened given the PR system. Consequently, the reasonwhy the symbolic gesture only came from deputies mustbe related to the lower threat to their incumbency.

Second, the law was not voted by parties but bydeputies themselves. The same politicians (from bothmain parties) who passed the law and proudly claimedto have brought French democracy to a new era, a fewmonths later heavily lobbied the party leaders to obtainthe right to run again. Were they unable in 2000 to antic-ipate that they would have huge incentives to circumventthe law in 2002? On the contrary, we view this as a proofthat they correctly anticipated that their inconsistencywould not be punished by voters. More precisely, it isquite likely, in our opinion, that most politicians antici-pated that they would benefit, at least in the next elections,from a larger incumbent advantage due to the increasedprobability of competing against a new woman candidate.

Third, if parity was demanded by voters, why didn’tthey punish the parties that did not comply with theparity requirement, or more precisely, how can we explainthe negative correlation between the fraction of femalecandidates and the success of the party?10

10The main right-wing party (UMP), winner of the 2002 election,presented only 19.93% of women and paid EUR 4M, representing15.8% of its government funding, while the main left-wing party(a coalition led by the socialist party), second main group at theAssembly, presented 36.13% of women and lost 9.1% of its fund-ing (see Jourdain 2002). The third party, UDF, also presented lessthan 50% of women and paid fees, whereas all other parties com-plied with the parity requirement. Note that in France campaignfinancing is very restricted, so that these reductions in party fundshave nontrivial consequences.


The literature on women’s low representation in par-liaments has concentrated on two main sets of explana-tions: those based on the electoral rules, and those basedon the functioning of and/or the competition betweenparties. On the other hand, it has almost disregardedexplanations based on voters’ preferences. The commonwisdom in the literature is that voters’ antipathy towardfemale candidates is not supported by the data (at leastin Western democracies; see, e.g., Darcy and Schramm1977; Hunter and Denton 1984; Kelley and McAllister1984; Rasmussen 1983; a counterexample, about France,is provided in Foucault 2006).11,12 The French case makesus stand in contrast with this literature, given our empir-ical finding of male advantage and given the explanatorypower of our constitutional design model based on sucha finding. However, the contrast is less sharp than it mayseem at first glance, since there is a simple story thatcould at the same time make sense of our theory andserve as reconciliation with the findings for other coun-tries in other studies: the parity law itself, by forcing par-ties to rapidly increase the number of female candidates,may have brought about an asymmetry in the perceivedquality of male and female candidates. Our data analysisshows that female new candidates at the 2002 electionswere easier to defeat than male new candidates. Giventhat France is the only country with such a parity law,this evidence is the only one we need to support ourmodel, and for the very same reason, it does not con-tradict any of the previous studies necessarily. Moreover,we also estimated the same bias with data from the 2007elections (see Table 3 below), and the male bias is stillsignificant but smaller, in line with the above hypothesisthat parity may create just a short-run advantage to maleincumbents.

We need to add, however, that two other find-ings (documented below) question the common wisdomabout absence of voters’ gender bias beyond the effectof parity itself just mentioned. First, we estimated thepossible male bias using the data from the elections be-

11In closed party-list systems it is obviously impossible to directlytest the existence of a male bias among voters, since voters vote forparties, not candidates. Hence the only systems in which voters’bias can be empirically tested on field data against party bias areplurality systems or open-list systems. Survey data can be collectedof course for both systems, but the reliability remains intuitivelyhigher for systems in which voters cast their ballot for individualcandidates.

12By antipathy, hostility or preference toward male or female can-didates, we clearly mean those revealed by actual votes. We do notexplore the reasons why voters would claim in interviews to bewilling to vote for this or that candidate. Evidence like that givenby Converse and Pierce (1986), for instance, is hardly related to ourundertaking.

fore the parity law was passed (see Table 3), and, evenif missing data prevent us from giving the same creditto those estimations, we find a significant male bias ofsimilar magnitude.13 Second, we estimated the possiblemale bias using 2002 data about all male and femaleincumbents. We surprisingly find a significant, thoughsmaller, male bias. Clearly, this cannot be due to theinjection in the system of new and inexperienced fe-male candidates. More work needs to be done in orderto conclude whether the male bias is induced by par-ity or associated with a persistent feature of the Frenchelectorate.14 This puzzle is important per se and will bedecisive for the long-run impact of parity on womenrepresentation.15

One may argue that the male bias we find does not re-flect voters’ but parties’ hostility against women. We callthis hypothesis “party bias,” and it is obviously relatedto the “male conspiracy theory” proposed in Duverger(1955). By systematically sending female new candidatesto less favorable districts than male candidates, indeed,parties can create the type of bias we have found. AfterLovenduski and Norris (1993), the literature on the lowrepresentation of women in Parliaments has highlightedthe responsibilities of parties, and in particular of theirorganizational and ideological barriers. A first challengeto that view comes from the fact that all French partiessupported the law (as far as the Assembly is concerned,and Senators from all parties criticized it). Most impor-tant, the main challenge comes from the data. Estimatingthe party bias is a difficult task, as it should be care-fully distinguished from the strategic use of the (male)incumbents’ advantage.16 The tests we present in the

13The male advantage in 1997 data is something that could havebeen known at the time of the reform.

14We remark that by voters’ persistent bias we do not refer neces-sarily to discriminating preferences, but to whatever reasons maymake voters have a net preference for men when all the other ob-servable variables are kept constant. For instance, voters’ bias canarise from a widespread belief that men bring more pork to thedistrict, whereas women are more concerned about global publicgoods, and the electorate of a district may prefer a focus on theformer type of policies.

15The indications that the male bias may be persistent in the pop-ulation should not be considered once again in contradiction tothe literature: our estimations focus on the Assembly elections,where competition is head-to-head. That the willingness to votefor female candidates is lower in this type of elections comparedto elections where women are part of a larger ticket is, after all, theimplicit assumption of the literature on the relationship betweenelectoral systems and women representation and on the superiorityof PR over SMD.

16Note that some authors (for instance, Murray 2004) consideras a form of party bias the fact that party leaders are not willingto deselect incumbents to replace them with female candidates.


second section show that new male candidates have notbeen placed in 2002 in districts more favorable to theirparty than new female candidates. Also, the latter have notreceived lower financial support from the parties than theformer.

Male Advantage and Voters’ Bias

This empirical section is divided into two parts. Thefirst section shows that in the last three elections for theFrench National Assembly there has been a significantmale advantage among candidates of otherwise similarcharacteristics. Let us recall that for the main point of thearticle to hold, and for the theoretical model to be mean-ingful, proving the existence of such a male advantageis all that matters. However, we will then provide someinteresting side results about the potential sources of theobserved male advantage.

Our data are mainly based on information collectedfrom the website of the French National Assembly.17 Thewebsite provides, among other things, biographical in-formation on candidates in 2002 elections, their partyaffiliation and incumbency status, and the district-by-district first- and second-round results in both the 1997and 2002 elections, together with abstention rate of eachdistrict. We have then collected the same data from the2007 Assembly elections, in order to verify whether thefindings from the 2002 data are robust or if there are sig-nificant changes.18 We have also obtained age data fromhttp://www.fluctuat.net/. Finally, some of the data weregiven to us by the Centre de Donnees Socio-Politiques. Inorder to avoid difficulties associated with variable numberof parties and the resulting strategic voting behavior, wefocus on those districts where election went to the secondround and where the two second-round candidates werefrom the two main party coalitions of the 2002 elections,

That is not the form of bias we are investigating as we conditionour analysis on the incumbency status of the candidates and weassume that parties, which are a collection of incumbents, favorthe reelection of incumbents (of any gender). Thus, if a party doesnot display any bias in favor of new men against new women inthe allocation of the districts where the party does not have anincumbent, then such a party is not biased in our sense, even if itdoes not deselect any incumbent.

17http://www.assemblee-nationale.fr/elections

18We have complemented this with party contributions data foreach candidate’s campaign from Publication Simplifiee des Comptesde Campagnes.

TABLE 1 Types of Runoffs

M vs M F vs F M vs F F vs M Total

New vs New 16 12 16 16 60New vs 97 Loser 30 4 2 2 38New vs Mover 14 0 4 4 22New vs Incumbent 186 22 73 73 35497 Loser vs Mover 8 2 1 1 1297 Loser vs Incumbent 67 2 14 20 103Mover vs Mover 2 0 0 0 2Mover vs Incumbent 2 0 1 1 4Total 325 42 111 117 595

PS and UMP.19 Table 1 gives some descriptive statisticsfor 2002 in terms of the frequency of the various “types”of runoffs.20

Male Advantage

The goal here is to establish the presence of male advan-tage in the 2002 elections. We will then see that somedegree of male advantage remains also in 2007, but to alower extent.

For observation/candidate j , we assume a linearmodel of the form yj = �X j + ε j . Different specificationsare estimated, but in the basic one yj is candidate j’s per-centage of votes (henceforth score) in the second round ofthe 2002 (resp. 2007) elections. Besides a variable measur-ing the male advantage, which we describe next, the vectorX j of controls includes the score in the second round ofthe 1997 (resp. 2002) election obtained by the candidateof the same district and same party as candidate j.21 Thisparty- and district-specific variable accounts for the ag-gregate preference toward a specific party within each dis-trict. It also serves the purpose of controlling for the factthat women might be sent to “worse” districts than men.A second control is age difference between opponentsin the same district, since a candidate’s age is plausiblycorrelated with his or her perceived quality or experience

19Only 10% of the districts assigned a seat in the first round.

20The letters M and F refer to the gender of the candidates; the term97 loser clearly indicates a candidate who had been a candidate be-fore but was not an incumbent; the term mover refers to a candidatewho was elected in 1997 but in another district.

21Thus we also eliminate some observations that have no suchcorrespondence in 1997, e.g., when no PS, RPR, or UDF candidatesran in that district in 1997 or if they were eliminated in the firstround. (Since the UMP did not exist in 1997, we use the score fromthe RPR or UDF.)


TABLE 2 2002 Scores: Significant Male Advantage

New Incumbent

Candidate (1) (2) (3) (4)

Own Party Score in 1997 0.550∗∗∗ 0.618∗∗∗ 0.508∗∗∗ 0.516∗∗∗

(0.052) (0.049) (0.044) (0.044)Male Advantage 0.009∗ 0.017∗∗∗ 0.013∗∗∗ 0.013∗∗∗

(0.005) (0.005) (0.004) (0.004)Age Difference/100 0.360∗ 0.350∗ 0.105 0.144

(0.187) (0.191) (0.169) (0.167)Difference of Square of Age/100 −0.004∗∗ −0.004∗∗ −0.001 −0.002

(0.002) (0.002) (0.002) (0.002)Party Right of Center 0.084∗∗∗ 0.079∗∗∗ 0.082∗∗∗ 0.081∗∗∗

(0.007) (0.007) (0.006) (0.006)Opponent is a New Candidate 0.033∗∗∗

(0.010)Opponent is a 1997 Loser 0.036∗∗∗ −0.007

(0.012) (0.005)Opponent was Moved −0.008 −0.026

(0.014) (0.029)Constant 0.166∗∗∗ 0.147∗∗∗ 0.233∗∗∗ 0.226∗∗∗

(0.025) (0.024) (0.025) (0.024)Observations 237 237 282 282

Standard errors in parentheses.∗significant at 10%; ∗∗significant at 5%; ∗∗∗significant at 1%.

(we deal with other indirect tests of the role of experiencebelow). We also control for the difference of the squareof their age.22 Finally, we control for party affiliations,since they could be correlated to the gender bias. This isdone by including an indicator variable that takes value1 if the candidate is from UMP and 0 if he or she is fromPS. A constant term is also included, which represents theaverage score of a candidate in 2002 (resp. 2007) when allother regressors were zero.23 Error terms (ε j) follow stan-dard assumptions imposed by the ordinary least squaresestimation method.24

22Both are divided by 100 to make results easier to present.

23We also considered controlling for the difference in campaignexpenditures between the candidates in the same district. Out ofthe eight specifications reported in Tables 2 and 4, adding this re-gressor had no qualitative impact on the male advantage estimates,probably because most candidates received amounts close to theirlegal upper bound. That is consistent with previous findings thatcampaign expenditures do not have significant effects on incum-bents’ scores (see Foucault 2006). Given this, and given that we donot have this data for 2007, this regressor has not been included.

24The fact that the dependent variable lies between 0 and 1 could beproblematic in an OLS regression if we had regressors with valuesin a large range. Here it is not a problem because the right-hand side

The key regressor is the male advantage. It can bemeasured by a variable that takes value 1 if a male has afemale opponent, 0 if the two candidates are of the samegender, and −1 if a female has a male opponent. We willalso show, although it is not crucial to our argument, thatthe implicit symmetry assumption—namely that womanversus woman is just like man versus man and that theadvantage of a man incumbent (respectively, new mancandidate) over a woman is equivalent to the disadvan-tage of a woman incumbent (respectively, new womancandidate) with respect to a man—is actually supportedby the data.

Table 2 reports estimation results for 2002. Specifi-cations (1) and (2) only use new candidates while speci-fications (3) and (4) use incumbents.25 Specifications (1)and (3) control for the type of the opponent (either a

is composed mostly of regressors between 0 and 1. Nonetheless, wehave also estimated the standard transformed equation ln(

y j

1−y j) =

�X j + ε j . The conclusions are unchanged (in particular the signand statistical significance of our measure of male advantage), thuswe prefer to report the more familiar and easier to interpret casewhere the dependent variable is not transformed.

25In specifications (1) and (2), since we limit attention to newcandidates, and since in each second round of each district election


TABLE 3 Male Advantage Before and After 2002

1997 2007

New Incumbent

Candidate (5) (1c) (2c) (3c) (4c)


(0.065) (0.059) (0.069) (0.068)Male Advantage 0.029∗∗∗ 0.008∗∗ 0.011∗∗∗ 0.007∗ 0.007∗

(0.008) (0.004) (0.004) (0.004) (0.004)Age Difference/100 −0.062∗∗ −0.044∗ 0.206 0.208

(0.025) (0.025) (0.149) (0.148)Difference of Square of Age/100 0.000∗∗ 0.000∗ −0.002∗ −0.003∗

0.000 0.000 (0.001) (0.001)Party Right of Center −0.032∗∗∗ −0.050∗∗∗ −0.048∗∗∗ −0.048∗∗∗ −0.047∗∗∗

(0.008) (0.006) (0.006) (0.005) (0.005)Opponent is a New Candidate 0.024∗∗∗


(0.012) (0.005)Opponent was Moved 0.003 −0.007

(0.023) (0.035)Constant 0.515∗∗∗ 0.171∗∗∗ 0.123∗∗∗ 0.177∗∗∗ 0.175∗∗∗

(0.006) (0.030) (0.028) (0.038) (0.037)Observations 346 204 204 229 229


new candidate, a 1997 loser, or a 1997 winner that wasmoved to a different district): for (1) the excluded cate-gory is an incumbent opponent and for (3) it is a newcandidate opponent. These dummies are jointly statisti-cally significant (p-value <0.1) in specification (1) butnot in specification (3) (p-value > 0.1), and thus we alsoreport (2) and (4) where those dummies are excluded.Own party score in 1997 and the party position are statis-tically significant in every specification. Not surprisingly,the effect of own party score in 1997 is positive.26 Age

the race is 91% of the time between a new candidate and someonewho is not a new candidate, only about 4% of the new candidatesneed to be dropped in order to avoid having two candidates fromthe same district (which would determine correlation between theerror terms). However, the results are basically identical with orwithout such a restriction of the sample. When more than one newcandidate ran in the same district, the selection rule was to selectmale candidates if they ran against a woman; otherwise it was toselect the candidate whose first name starts with the earliest letterin the alphabet.

26One effect of the male bias could be to affect party allegiance asa function of the gender of the candidates, which would suggestinteracting own party score in 1997 with gender. We cannot reject

difference has a positive impact on score for both newcandidates and incumbents, but is statistically significantonly for new candidates.

The main finding is a statistically significant male ad-vantage, which is observed for both new candidates andincumbents irrespective of the specification.27 Table 5shows how this effect differs when a woman faces awoman, a woman faces a man, and a man faces a woman,from the baseline where a man faces a man. We show thatthe hypothesis that woman versus woman is not differ-ent from man versus man and that the advantage of aman versus a woman equals the disadvantage of a womanagainst a man cannot be rejected (this is termed the sym-metry hypothesis in the table). In the same table, one can

the null hypothesis that the effect of score in 1997 is the same formales and females in specifications (1) through (4).

27Interacting “Male Advantage” with “Party Right of Center” indi-cates that there are either no differences in terms of the impact ofthe male advantage on score across parties (specifications 2 and 3)or that it is more severe for the PS (statistically significant at the10% level for specifications 1 and 4).


TABLE 4 Male Advantage on Probability of Winning (Logit)

New Incumbent

Candidate (6) (7) (8) (9)


(3.484) (3.215) (4.117) (4.067)Male Advantage 0.729∗∗ 0.962∗∗∗ 0.761∗∗ 0.856∗∗∗

(0.320) (0.299) (0.326) (0.318)Age Difference/100 17.314 14.504 26.715∗ 30.371∗∗

(12.985) (12.818) (15.074) (14.942)Difference of Square of Age/100 −0.190 −0.156 −0.282∗ −0.314∗∗


(0.673) (0.550) (0.899) (0.891)Opponent is a New Candidate 1.116∗

(0.666)Opponent is a 1997 Loser 1.528∗ −0.623∗


(0.879) (1.489)Constant −10.380∗∗∗ −10.451∗∗∗ −13.080∗∗∗ −13.351∗∗∗

(1.879) (1.731) (2.240) (2.216)Observations 237 237 282 282


notice from columns 3b and 4b that female incumbentssuffered a statistically significant disadvantage.

One question to ask is to what extent the male ad-vantage is a stable phenomenon or to what extent it wassimply a transient one, perhaps determined by the sud-den influx of less-experienced female candidates due tothe introduction of parity. Table 3 presents results forthe 1997 and 2007 data. For 1997 we cannot separatenew candidates and incumbents and many regressors aremissing. Table 6 presents regressions that help us to assessthe bias in the estimate of male advantage in the 1997 datadue to the confounding of incumbency and male advan-tage as well as the impact of the other missing regressors.Specifications (10) and (11) divide the data by party andinclude a dummy regressor for incumbency. This allowsus to see that the male advantage is about two-thirdsof the incumbency advantage. Specification (5b) mimicsthe 1997 specification using the 2002 data. This gives anestimate of male advantage about 25% higher than theestimate in 1997 and thus suggests that the male advan-tage prior to the 2002 election might have been slightlyweaker. Clearly, the data from 1997 and 2007 do not al-low us to reject the hypothesis of a stable presence of maleadvantage.

Coming back to the 2002 data, one interesting ques-tion is to what extent the male advantage mattered, look-ing for the impact of gender on the probability of winning.Table 4 presents logit estimates of the determinants of awin (win equals one and lose equals zero) using the sameregressors as for the specifications presented in Table 2. Inboth specifications (6) and (8) the joint hypothesis thatthe effect of the type of opponent (new, 1997 loser, orwas moved district) is equal to zero cannot be rejected(p-value > 0.1). For both new candidates and incum-bents, all other regressors have the expected sign and arestatistically significant. For a male, having an opponentof opposite gender increases the probability of winning—and for a woman it decreases it. The popularity of a can-didate’s party in 1997 has a significant positive effect. Theolder the candidate with respect to his or her opponent,the more likely he or she is to win, but this effect is de-creasing as the age difference increases. Finally, everythingelse being equal, the UMP candidates were more likely towin in 2002.

To summarize, men have a statistically higher scorewhen they face a female candidate. A man facing a womangets between 1 and 2 percentage points boost in his scorecompared to a case where he faces a man. Although


TABLE 5 The Effect of Male Bias on Scores

New Incumbent

Candidate (1b) (2b) (3b) (4b)


(0.052) (0.049) (0.045) (0.044)Male Candidate with Female Opponent 0.011 0.023∗∗ 0.012∗∗ 0.013∗∗

(0.010) (0.009) (0.006) (0.006)Female Candidate with Male Opponent −0.009 −0.013∗ −0.015∗ −0.016∗

(0.007) (0.007) (0.008) (0.008)Female Candidate with Female Opponent −0.010 −0.003 0.013 0.014

(0.011) (0.011) (0.012) (0.012)Age Difference/100 0.373∗∗ 0.359∗ 0.113 0.149

(0.187) (0.192) (0.169) (0.167)Difference of Square of Age/100 −0.004∗∗ −0.004∗∗ −0.001 −0.002


(0.007) (0.007) (0.006) (0.006)Opponent is a New Candidate 0.034∗∗∗



(0.014) (0.029)Constant 0.168∗∗∗ 0.145∗∗∗ 0.236∗∗∗ 0.230∗∗∗

(0.025) (0.025) (0.025) (0.024)Observations 237 237 282 282F-Test of Symmetry Hypothesis (p-values) 0.610 0.708 0.496 0.425


this advantage may seem small in magnitude, it had animportant impact for the candidates’ probability of win-ning in 2002. Using specification (7) we compute theprobability of winning for a new male candidate whoruns against a female to be 22 percentage points higherthan against a male (this is computed setting all otherregressors at their sample mean values).28 Similar com-putations using specification (9) reveal that the equivalentgain for incumbent males is 10 percentage points.

Causes of Male Advantage: Experience,Voters’ bias, Party bias

In this section we highlight what our data analysiscan yield in terms of the likelihood of the various

28To see how the roughly 1 to 2 percentage point difference can beconsistent with the 22% probability difference, note that more than10% of the runoffs have a victory margin of less than 2 percentagepoints, and roughly 25% of runoffs yield more than 47.5% of votesto the loser.

sources of male advantage that one could intuitively referto.

As already pointed out in the introduction, the maleadvantage we have identified among incumbents tendsto prove that differential experience cannot be the onlysource of the male bias. Moreover, we estimated specifi-cations (1) and (2) on a subsample of young candidates(more specifically, using the subsample of candidates whoare younger than the youngest incumbent in our sample).The estimates of the male advantage are still statisticallysignificant (and the coefficient estimate is actually largerat about 0.028 and 0.023 in each specification), in spiteof the fact that in that subsample the office-holding ex-perience must be minimal for any gender (although ofcourse there could still be some unobservable systematicdifferences at local or regional levels).

Next, we reject the hypothesis that the male bias in2002 comes from a party bias. This hypothesis consistsof asserting that the difference in the score of female


TABLE 6 The Incumbency Advantage in 2002

PS UMP PooledCandidate (10)a (11)a (5b)

Own Party Score in 1997 0.650∗∗∗ 0.541∗∗∗

(0.044) (0.053)Incumbent Advantage 0.022∗∗∗ 0.030∗∗∗

(0.007) (0.010)Male Advantage 0.015∗∗∗ 0.020∗∗∗ 0.040∗∗∗

(0.005) (0.006) (0.005)Age Difference/100 0.386∗∗ 0.040

(0.169) (0.210)Difference of Square of Age/100 −0.004∗∗ −0.001

(0.002) (0.002)Party Right of Center 0.051∗∗∗

(0.007)Constant 0.134∗∗∗ 0.259∗∗∗ 0.457∗∗∗

(0.021) (0.024) (0.005)Observations 207 207 349

Standard errors in parentheses.∗significant at 10%; ∗∗significant at 5%; ∗∗∗significant at 1%.a Only includes incumbents and new candidates.

candidates can be due to females being sent by bi-ased party leaders to less favorable districts. Note firstthat our regressions control for the score of the partyin the candidate’s district in the previous election, andhence, unless there are important changes in betweenelections in terms of which districts are difficult towin, the regressions themselves are already basicallyseparating the male advantage from the party- anddistrict-specific characteristics. A party bias would takethe form of a correlation between gender and the ex-pected score of candidates. In Figure 1, we divide the

FIGURE 1 Percentage of New Male 2002Candidates as a Function of 1997Score of Own Party

range of 1997 scores into intervals of 2.5% and presentthe ratio of new men candidates in districts falling ineach interval. It turns out that women are sent to dis-tricts where the average 1997 score is equal to 44.7%while men average is 45.5%. Both a t-test (p-value =0.31) and a Wilcoxon/Mann-Whitney test (p-value =0.17) cannot reject that the two are equal.29 In otherwords, no party has shown a biased preference for menover women in “good” districts where it did not have anincumbent.

In contrast with the 2002 elections, in 2007 we findsome evidence of party bias: the 2002 score of the districtswhere women were sent as candidates in 2007 averaged45.8%, and for men it is 47.9%. These are statisticallydifferent using both the t-test (p-value = 0.005) and theWilcoxon/Mann-Whitney test (p-value = 0.017).

Another way parties could treat women differently isby giving them less funding for the campaign. There does

29In a previous version of the article, available at http://homepages.nyu.edu/∼gf35/print/fmm 2006.pdf, we consider otherways to determine the presence of party bias. We also explore thepossibility of party strategic behavior given the existence of a maleadvantage (which would suggest a tendency for parties to place menin close races and women in uncontested races, but without assign-ing disproportionately the good districts to men). We concludedfrom that analysis that there is little to no evidence of party biasor of strategic behavior, and in relative terms strategic behavior isslightly more likely.


not seem to be any evidence of this in 2002. In fact, oneparty gave on average more to its female candidates. Thereis, however, a big difference across parties. The UMP gave10,000 Euros to many of its candidates (the median ofwhat it gave is 10,000 Euros) while the PS gave nothing toa majority of them (its median is 0). The UMP gave onaverage 9,443 Euros to its female and 9,423 Euros to itsmale candidates. The PS gave 1,496 Euros and 1,730 Eurosto its female and male candidates, respectively. Using at-test, for neither party are these numbers statisticallydifferent, while using the Wilcoxon/M-W test it is at the10% level for the UMP (in which case women were treatedmore favorably than men). Given the conclusion that theexperience factor and party bias were not relevant norpresent in 2002, it leaves voters’ bias as the most likelyexplanation for the male advantage.

A Model of Constitutional DesignIncentives for Assembly Incumbents

The Assembly deputies are elected with a two-ballot ma-jority rule. In order to avoid having to deal with strategicvoting, in our model we assume that there are only twoparties, so that the system is equivalent to one-ballot plu-rality. Downs (1957) defines a political party as “a coali-tion of men seeking to control the governing apparatusby legal means,” where by coalition he means “a group ofindividuals who have certain ends in common and coop-erate with each other to achieve them.” A simple way tooperationalize this definition in a theoretical frameworkis to view a party as a “coalition of incumbents seeking re-election.” Given the importance of incumbent politiciansin any party hierarchy, it is clear that any party leader willhave at least two objectives in mind when choosing thecomposition of the party candidate list: the maximiza-tion of the number of seats the party will obtain and themaximization of the chances of reelection of the party’sincumbent politicians.30 For simplicity we will also as-sume that all incumbents are men.

The crucial simplifying assumption of the theoreticalmodel is that if a man candidate runs against a woman, heis elected no matter what the voters of that district thinkof the candidates’ policy platforms. This very strong form

30The assumption that parties care about the number of seats ob-tained by their policy platform as well as about the probabilityof reelecting incumbents will be kept in order to make the modelsolvable. After proving our formal proposition using this simplifiedparty objective, we will discuss the implications of extending themodel to more complex but perhaps more realistic assumptionsabout the internal hierarchy of parties.

of male bias is assumed in order to make computationsmanageable, but the qualitative results do not change if aweaker form of male bias is considered.

Before turning to the more general model, it is im-portant to illustrate the basic intuition. Suppose that wejust needed to explain why men incumbents can prefera “pure” parity law to the status quo without parity. Wecould give the explanation by means of a simple exam-ple: suppose that the country is divided into two districts,so that the Assembly is composed of two incumbents,i.e., the previously elected deputies of those two districts;suppose also that the two incumbents are of the two ma-jor parties and that they must run in the district wherethey were elected (either because it would be illegal orbecause voters would punish such a switch). If no paritylaw is passed, the chances of reelection of an incumbentdepend on the realization of voters’ policy preferences inhis district, whereas if a pure parity law is passed, eachincumbent is sure to run against a woman (as the menquota will be used by the other incumbent running in hisown district), and hence there is an additional advantage,inducing a higher probability of reelection (probability 1in the case of the extreme gender bias mentioned above).However, explaining why they passed a law that allowsparties to pay fees to violate parity is not possible bymeans of a simple example and requires a more explicitanalysis of all the politicians’ incentives.

Let the two parties be denoted by L and S. There is aset [0, 1] of districts. The current Assembly is composed ofthe candidates who were elected in the previous electionsand are still in office. Districts in [0, �) have an incumbentof party L, whereas districts in [�, 1] have an incumbentof party S. We assume without loss of generality that � ≥0.5 (party L is the large party).

At time 0, the deputies vote for a value of c ∈ [0,∞], the fee a party needs to pay to circumvent parity ina district. If c = 0, there is no limit to the number ofmen running in the country for the same party, that is,there is no parity requirement (the status quo). If c = ∞,it is illegal to have more than 50% of men running, thepure parity case. If 0 < c < ∞, the law allows parties tosend men to any extra measure of districts beyond 50%provided the party pays fees equal to c times that extrameasure. We need to prove that the vote outcome can be apositive and finite c, such that fees are paid in equilibriumunder some realization of policy preferences.

At time 1, lists are composed. That is, each partydecides whom to run in each district. Incumbents are as-sumed to rerun in their district if their party decides torun a man in that district. Also, we assume that incum-bents cannot shift from their home district to anotherone. Consequently, if a man runs in a district where the


party did not win the previous election, then this man isa new candidate.31 At time 2, voting takes place. In eachdistrict, voters vote for the candidate they prefer. Thereare only two candidates in each district, hence no strategicvoting takes place.

Voters differ in their platform preferences, which canchange over time, but they also have very strong genderpreferences: being in favor of the platform of one partytranslates into a vote for that party unless that party’scandidate is a woman running against a man. In the timeelapsing between time 0 and time 2, voters’ platform pref-erences may change. At time 2, districts [0, z) prefer theplatform of party L, and [z, 1] are in favor of the platformof S. The implicit assumption here is that in any possiblenew realization of voters’ platform preferences it cannothappen that district i has a majority of S platform sup-porters and a district i′ > i has a majority of L supporters.This order assumption allows us to simplify the treatmentof uncertainty at time 0, since in this way the uncertaintyis just about the parameter z. The uncertainty about z isgreater at time 0 than at time 1. For simplicity, we assumethat it is known at time 1, whereas only the probabilitydistribution is known at time 0.32

The utility of an incumbent of party p, p ∈ {L, S},depends on the fraction of seats obtained by his party inthe time 2 election, denoted by N p; on whether or nothe is reelected; and on the budget of the party, which isaffected by the total cost paid by the party to circumventparity, denoted by C p. Formally, for all i ∈ [0, �)

Ui = U (NL ) + a Ii − CL

�(1)

where a is the utility of being reelected, I i is the indicatortaking value 1 if i is reelected and 0 otherwise, and U(N)denotes the utility that i derives from the fact that hisparty obtains a fraction N of the seats. Even though theresult could be proved with any U(N) weakly convex forall N ∈ [0, 0.5) and weakly concave for all N ∈ (0.5, 1],the following functional form is the simplest to consider

31The implicit assumption is that incumbency is local and does notconstitute an advantage if one switches district. The little evidenceof incumbents running in different districts from the one wherethey had been elected confirms that this assumption is realistic,but the qualitative results of our model hold even when we allowincumbents to do this kind of shift, but with useless additionalcomputation complexity.

32No result depends on the simplifying assumption that z is knownat time 1. Everything would go through in a similar manner if attime 1 there were a less precise update.

(letting b be a real number in [0, 1)):

U (N) = bN if N < 0.5

0.5 if N = 0.5

1 + bN if N > 0.5.

For all i ∈ [�, 1]

Ui = U (NS) + a Ii − CS

1 − �. (2)

Consistent with the Downsian view of a party dis-cussed at the beginning of this section, we define a partyas the aggregation of its incumbents. Consequently, weassume that the utility of a party is the sum of the utilitiesof its incumbents:

UL = �U (NL ) + a IL − CL , (3)

and

US = (1 − �)U (NS) + a IS − CS (4)

where I p stands for the number of reelected incumbentsof party p, p ∈ {L, S} .

Parity means that there needs to be 50% of candidatesof each gender for each party. Any deviation from thatgender distribution entails a marginal cost of c, so that

C p = c | Mp − 0.5 |, p ∈ {L , S}where M p is the fraction of men candidates of party pselected at time 1.

Given all the assumptions above, we have our maintheoretical finding:

Proposition 1: If b is small and a is large (i.e., reelectingan incumbent is important for a party but the marginalutility of a new seat is small unless it allows the party to ob-tain the majority), then there exist well-behaved probabilitydistributions of voters’ platform preferences such that, at theconstitutional choice stage (at time 0), a “parity with fees”system is unanimously preferred to the no-parity system,and is preferred by a majority to the pure parity system.

The formal proof is in the appendix. The intuitionis similar to the one given for the two-district case as faras the reason for preferring pure parity to the status quo.The intuition for the additional result that parity with feescan dominate even pure parity is as follows: given that aparty is a coalition of incumbents and hence reelectingincumbents has priority over electing new candidates,the larger party wants a parity law in order to protect itsincumbents in the states of the world in which platformpreferences happen to favor party S, but given that L’sincumbents are more than 50%, pure parity is dominatedby a system where even the other � − 0.5 incumbents can


be protected (with some probability) by paying fees. Asmall b and a relatively large a are needed so that thereexist values of c for which parties are ready to pay the feeonly if it allows an incumbent to run: indeed, if no suchvalue of c exists, parity with fees cannot be optimal aseither the party would refuse to pay to allow one moreincumbent to run, or, if the party pays, the opponentparty also pays and the incumbent runs against a man,thereby losing his seat anyway. There are restrictions onthe class of admissible distribution functions because theuncertainty to be reelected needs to be sufficiently large: ifa large fraction of incumbents is sure to be reelected, theymay have no incentive to pass the law as it doesn’t increasethe probability that their party wins the election, and it islikely to impose a cut in the budget of the party. However,as one can verify in the appendix, the conditions on a, b,and on the skewness of the probability distribution toobtain consensus on parity with fees are very reasonable.

As a corollary of proposition 1, one could easily checkfrom its formal proof that the expected number of womenelected given parity law (with fees allowed) is zero. Theresult is thus very sharp: not only is the parity law as itpassed in France perfectly consistent with the self-interestof the male incumbents, as proved by proposition 1, butit is also completely ineffective in terms of the officialgoals. Of course, using a less extreme type of gender biasthan that of this simple model, we could determine apositive (but small) number of expected women elected.In fact, the model could be easily extended relaxing theassumption that a male candidate always wins againsta female candidate. We could assume instead that, whenvoters prefer the political platform of his opponent’s party,a male candidate’s probability of winning is some interiorg > 1/2 if the opponent is a woman.

Leaving probability 1 of victory in the easier casein which platform preferences are also in his favor, theonly change would then be that the expected utility forthe party at time 1 of having one additional incumbentrunning in a district where the voters’ preferences haveswitched decreases. Consequently, the optimal parity withfees system would become one associated with a lowerc. The equilibrium number of women elected would bestrictly positive (but small) in this simple extension. An-other (more interesting) extension could be to assumethat parties are “more” than a simple coalition of in-cumbents. There may well be other potential candidates,besides the incumbents, whose election would increasethe party utility by b + a, and who come from districtswhere the other party has an incumbent.

Such an extension is particularly relevant for France,as many right-wing deputies elected in 1995 lost theirseats in 1997 due to the huge (unexpected) victory of the

socialist party, and ran again in 2002.33 Given the marginalutility for a party to have those candidates running, theequilibrium number of fees paid by the parties increasesfor most values of z, with the possible outcome that bothparties pay fees simultaneously, in accordance with whathas been observed. This would not affect, however, ourmain result. Indeed, even if the probability of having torun against a man increases (as the opponent party ismore likely to pay the fee and have a male candidate), itis still optimal to have a parity with fees system as it bothguarantees that incumbents are still allowed to run, andit increases their probability of running against a woman,in the case where no opponent party member looks forelection in that district.

An important corollary of our proposition is thatparity may affect the party composition of the Assembly(and hence policies) when voters’ platform preferenceschange with respect to the status quo. The number ofseats won by the large party that is losing support interms of platform preferences is (weakly) larger than ifparity was not applied. Thus, the introduction of parityreduces the variance of party composition.

The ex ante and ex post Incentivesof Senators

In the previous sections we have first proved empiricallythe existence of male bias in the electorate, and then wehave shown how the ex ante incentives of deputies andthe ex post results were both consistent with a simplerational choice explanation based on male bias itself. Inthis section we aim to show the corresponding incentivesof Senators, although no formal model nor empirical testsare necessary for this chamber.

A Senator’s term was nine years at the time of the2002 elections (it was reduced to six years in July 2003),and a fraction of the Senate is recomposed every threeyears. The country is divided into a few large districts,and, depending on the population of the district, a num-ber of Senators, ranging from 1 to 12, is elected in eachdistrict. If the number of seats to be allocated is equal toor below a threshold, then a two-round plurality system isin order and parity does not apply. If the number is abovethe threshold, then the system is closed-list proportionalrepresentation (CPR). In this case, parity means that in aparty list there cannot be two consecutive candidates of

33In 129 districts out of the 361 we analyze, there was a candidatewho had lost in 1997.


the same gender. The threshold was equal to two in 2001and to three in 2004.

An essential feature of the senatorial elections is thatthe set of voters is composed of grands electeurs only, andabout 95% of them are municipality deputies. They hadno say in the passing of the parity law, but they tried toinfluence it through their Senators. Municipal electionsare two-round list elections. A list can run in the secondround if it obtains 10% or more in the first round. Theseat allocation rule is proportional with a 50% seat bonusto the winner. For instance, if a party wins the second-round elections with 40% of the votes and 60 seats areto be allocated, then it will get 30 + (0.40 ∗ 30) = 42seats, and the remaining 18 seats are allocated among theother parties proportionally to their second-round score.The implementation of the parity law at the municipallevel has this property: out of each set of subsequent sixcandidates in a party list, three have to be women. Theonly freedom which is left to the parties is the position ofthe women within each set of six candidates. Given theelectoral rule and the amounts of seats allocated in eachmunicipality (varying between 29 and 67), the parity lawis bound to have a huge effect on the gender compositionof the municipal assemblies, and a lot of incumbents mustlose their seat. A fraction of them must be thrown out ofthe list.34 Under the pressure of their grands electeurs,Senators obtained the amendment that parity would notapply in municipalities with less than 3,500 inhabitants,whereas Assembly deputies first proposed it to apply toall municipalities with more than 2,000 inhabitants. Sen-ators also proposed to remove the three women out of sixcandidate rule, but it was maintained. The percentage ofwomen elected in the municipalities with more than 3,500inhabitants went up from 25.7% to 47.5% (thereby mak-ing the fraction of women elected in municipal councilsrise from 21.7% to 33%).

Protecting their electorate was not the only concernof the Senators: they also had to protect their own seats.35

Out of the 74 (resp., 72) incumbent Senators looking forreelection in 2001 (resp., 2004) in districts where CPR ap-plies, only five (resp., 8) were women. Before the law waspassed, Senators tried to obtain the amendment that noalternating gender rule apply for the senatorial elections,

34The intuitive reason for the effectiveness of parity with a two-round CPR system with majority bonus is that with this system mostmunicipalities ended up with one party holding a large majority ofthe seats, and if—say—the elected members of such a party are 30,the law described in the text makes sure that 15 of them are women.

35The simple computations contained in this section use the elec-toral outcomes presented on the website of the French senate,http://www.senat.fr/. The details of the computations are availableupon request.

but failed.36 Nevertheless, only 20 seats—28%—(resp.,26—32.9%) went to female candidates. Given the num-ber of districts where parity does not apply and the loweffectiveness where it applies, the percentage of women is16.6%.

What did Senators resort to, in order to circumventthe law? The answer is what we call party proliferation.37

Out of the 29 districts where proportional elections wereheld in 2001 or 2004, party proliferation (incumbentspreviously elected under the same flag now running un-der different ones) took place in 11 of them. In eightother cases candidates elected on different lists registeredas members of the same senatorial group after the elec-tion.38 Finally, in several other districts, candidates pre-viously active in the same party, though new in the sen-atorial race, ran on different lists, with two examples ofsuch lists obtaining more than 10%. Party proliferationhas clearly been a wide phenomenon in both elections,which explains the low effectiveness of parity (see Sineau2002).39

Let us now analyze more closely the phenomenonof strategic party proliferation in CPR. We first describethe conditions under which party proliferation is mostlikely to happen. Then we study its effect on the partycomposition of the Assembly.

Party Proliferation

The cost of creating a party is relatively low for the Sen-ators. Given the grands electeurs system and the size ofthe districts, the actual number of votes needed to obtaina seat varies between 260 and 892. Moreover, those are

36Senators have a weaker role in France relative to many other coun-tries. This is clearly visible in Title V, Article 45 of the Constitution:“If the joint committee does not succeed in adopting a commontext, or if the text is not adopted as provided in the preceding para-graph, the Government may, after a further reading by the NationalAssembly and by the Senate, ask the National Assembly to make afinal decision.”

37This is best illustrated by the Meurthe-et-Moselle district, wherefour seats had to be allocated. Two right-wing incumbents had beenelected under the same party flag before. They split the list, createdtwo new parties, ran on the top of their respective list (followed, asrequired by the law, by a woman), and got reelected.

38Even though by definition those examples involve new candi-dates to the senatorial elections, these candidates do typically haveincumbent-type advantages, as they are former ministers, deputies,region presidents, etc.

39Proliferation of party lists has probably been made easier by thefact that Senators have a unique type of (small) electorate, thegrands electeurs. However, Jones (2004, Table 2) shows, amongother things, that some kind of list proliferation also took place inCosta Rica after the introduction of gender quotas (excluding themain two parties).


councillors themselves and Senators have regular oppor-tunities to meet them. Let us consider a party likely to ob-tain a score of s and an associated number of k seats, withk male incumbents. Let k be an even number. It seemsreasonable to assume that the incumbent’s advantage isdecreasing among candidates from the leader of the listto the kth elected: popularity decreases with rank. Givenparity, only k

2 incumbents can be given positions amongthe first k positions, those leading to a seat with some like-lihood. Therefore, the ( k

2 + 1)th incumbent is pivotal inthe proliferation process. His only chance of being electedis in creating his own list and diverting at least s

k+1 votersfrom the main party. This score is necessary, as the score ofthe main party, down to ks

k+1 , is otherwise still superior tok times that of the dissident list. This may not be sufficient,however, since other parties may have a larger d’Hondtscore for the last seat and obtain the formerly kth seat ofthat party. To illustrate this fact, let us consider a districtwhere three parties compete for eight seats and the dis-tribution of scores is (45,27.5,27.5), so that the allocationof seats is (4,2,2). After the parity reform, incumbent 3 ofthe first party is ejected from the first positions on the list.By running on his own and obtaining 10% of the votes,which corresponds to scores (35,10,27.5,27.5), he wouldkeep his seat. If we compare that result with the situationwhere there is only one opponent party and the scores are(45,55) before parity and (35,10,55) after proliferation byincumbent 3, we now have a distribution of seats goingfrom (4,4) to (3,0,5). The lower bound in the second situ-ation is now 11 and the scores (33.9,11.1,55) then lead to(3,1,4). Let us also note that any two incumbents ejectedfrom the main party list have no incentive to create a jointlist, as, given parity, their joint list would have to win threeseats for them both to be elected. Let us assume that the( k

2 + 1)th incumbent is sure to keep his seat if he createshis own list. Then the probability that the k

2 th incumbentis elected on the main list decreases, as the new score ofthe main party may no longer be sufficient to obtain k −2 seats. Moreover, if the ( k

2 + 1)th incumbent is able to beelected by running on his own, then so is the k

2 th incum-bent, given the assumption that individual popularity de-creases with the rank. The prudent strategy by candidatek2 is therefore to create his own list too, which, in turn, de-creases the probability of the ( k

2 − 1)th incumbent to beelected.

From this simple argument we can infer that prolif-eration is more likely the more popular is the ( k

2 + 1)thincumbent, but the unravelling may determine a situa-tion in which the incumbents who actually are observedmaking the split are higher in the rank. If k is large,it may be impossible to have a sufficiently large popu-larity for the ( k

2 + 1)th incumbent and, at the same

time, a decreasing order of popularity. This leads to thefollowing:

Remark: Party proliferation is more likely when (1) theincumbency advantage is more equal among candidatesand (2) the number of incumbents on the list, and/or thenumber of seats expected by a list, is lower.

The example and the reasoning above all assume thatthe scores are perfectly expected. Proliferation is also morelikely when the uncertainty of being elected by runningon one’s own is lower. When the number of seats to beallocated in a district and the number of relevant partiesare larger, then the competition for the last seats to allocateis larger, which increases the uncertainty.

This explains why, given that districts have on averagea relatively small number of seats, parity had low effect inthe senatorial elections.

Assembly Composition Effect

Parity may also affect the Assembly composition underCPR. There are two different effects. One is the large-party effect, which plays in a similar way as under SMD: ifa party has more incumbents than half the total numberof seats, then it has to lose the votes associated with theincumbency advantage of the incumbents it ejects fromthe list. Clearly, this may affect the score of the party, and,therefore, the number of seats it expects.

The second effect is directly associated with partyproliferation. In the example above, proliferation by in-cumbent 3 led to a change in the Assembly compositionfrom (4,4) to (3,0,5), which means a shift of one seat fromleft to right. The example may look extreme, as the pro-liferation was a failure. However, other examples may begiven of successful proliferation affecting the Assemblycomposition. Consider a district where two parties com-pete for six seats. The expected scores are (43,57), whichwould lead to a (3,3) allocation of seats. Assume that,indeed, there are three incumbents out of each platform.Again, we may think that incumbent 3 of the left partycan profitably create his own list, thereby preventing in-cumbent 2 from keeping his own seat. The equilibriumlist composition is therefore one where the left party hassplit into two lists, led by incumbents 1 and 2, respectively.Let us assume that the resulting distribution of votes is(24,19,57), and the resulting seat allocation is (1,1,4): pro-liferation by left incumbent 2 is successful, but increasesthe number of seats obtained by the right party.

The composition effect arising from the conflictinginterests of an incumbent seeking to keep his seat and a


party seeking to maximize the number of seats obtainedby candidates sharing its platform is likely to affect bothlarge and small parties. It is well known that under thed’Hondt system a party can never gain by splitting, as thed’Hondt coefficients cannot rise as a result of a split. Onthe other hand, as it is clear from the example, prolifer-ation is more likely to result in a loss of seats when thed’Hondt coefficient of the party as a whole is the lowestamong all parties.

Other Implications

The above characterization of party proliferation hassome implications for the advocates of gender quota leg-islations. Given that the probability of success after thecreation of a new list is obviously lower when there is aminimum threshold necessary to obtain seats, one canconjecture that a system with PR, large districts, and aminimum threshold is the most desirable for representa-tion purposes, although in a closed-list system the detailsof the law in terms of placement rules are crucial. Anotherway to create barriers to party proliferation is by enlargingthe districts and, correspondingly, the number of seats toallocate in the districts. First, this reduces the expected in-cumbent’s advantage of the pivotal incumbent. Second,as the number of competing parties is larger in largerdistricts, the competition for the last seats to allocate islarger, thereby increasing the sensitivity of the total num-ber of seats obtained by a platform to the way the totalnumber of votes is divided between the lists obtained byproliferation from one party.

Concluding Remarks

The common criterion used to evaluate representationreforms is the effectiveness of the reform. In the literatureon descriptive representation the objective to increase thenumber of women in politics finds many justifications.40

Among the countries where voluntary or mandatory gen-der quotas have been attempted, it is clear that the highesteffectiveness has been achieved in countries using PR withlarge districts (see, e.g., Jones 2004, Table 1). It is, there-fore, tempting to advocate for changes in the electoralsystems toward more proportionality, larger districts, andclosed lists.41 Our article moderates this conclusion by

40On the problem of underrepresentation of women in Parliaments,see Siaroff (2000) and Rosenthal (1995).

41We focus here on women representation, whereas a reform ofthe electoral system clearly involves multiple considerations. See,

focusing on the incentives to pass gender quota reformsunder different electoral systems for the incumbents.

The incumbents were interested in not losing theirpositions, and deputies knew they were the least chal-lenged by the reform. Had they passed a pure parity sys-tem without allowing for per-violation fees, and had therebeen a demand among voters for new female candidates,then of course the law would have been effective. On theother hand, had the reform been more likely to be effec-tive, then deputies would have shown the same oppositionto the law as Senators have. Our analysis thus highlightsthe following trade-off: when voters are not ready to favorfemale candidates, reforms are more likely to be passed incontexts where the electoral system will not make themeffective.42 This trade-off is something we expect to bepresent everywhere given the self-interest of incumbents,and could inspire future comparative analysis of reforms.

A final set of remarks can be made on the compari-son between France and other countries that use single-member district elections for their members of Parlia-ment. A natural question is why parity law has come upin France and not in other countries with similar elec-toral systems for their deputies. Our conjecture is thatthis may have to do with the perceived gender preferencesof the electorate. In the United States, there seems to beno evidence of voters’ hostility against women, nor muchevidence in favor of the male conspiracy theory. Thus,there is no “demand side” clear explanation for the lownumber of women in politics (see, e.g., Darcy, Welch, andClark 1994; Welch et al. 1985). Implicitly this implies amostly “supply side” story for the United States. The sharpcontrast between our study on the French case and theearlier studies on the United States43 suggests an intrigu-ing hypothesis to be tested in future research: countrieswhere voters’ gender bias exists have fewer women than

for instance, Morelli (2004) for a suggestive welfare comparison ofelectoral systems.

42SMD is not the only system where parity is unlikely to be effective:in an open-list electoral system, the strong and well-establishedincumbents have no worries because the order in the lists does notmatter (see the case of Belgium). Even within the set of countriesusing closed-list PR, countries with smaller electoral districts orcolleges should be more likely, by our considerations, to approveparity laws with respect to systems with larger ones, and perhapsthis could be used to explain why Spain is making more progressin this dimension with respect to Italy, for instance.

43Note that our empirical analysis is based on field data, whereasthe studies just mentioned on the United States are based on sur-vey data, and we have no way to say to what extent these sharpdifferences could be due to this.


men because of a “demand” bias and are more likely to en-dogenously generate affirmative action laws; on the otherhand, countries like the United States where no voters’demand bias exists, and where therefore the shortage ofwomen in politics is a “supply” issue, are unlikely to havethe necessary conditions for the approval of a parity law.

Appendix

Proof of Proposition 1. Once z is known, the country isconceptually divided into three regions: [0, min {z, �});[min {z, �}, max {z, �}); and [max {z, �}, 1]. PartiesL and S play a list composition game, and a strategy isan assignment of a man or a woman in each district.Formally, a strategy is an element of {0, 1}[0,1] where 0(resp. 1) means that a woman (respectively, a man) is sent

to that district. Denote by mjp ∈ [0, 1] the fraction of men

candidates running for party p, p ∈ {L, S}, in region j, j∈ {[0, min {z, �}), [min {z, �}, max {z, �}), [max {z,�}, 1]}.

Given our assumptions on voters’ platform prefer-ences and gender preferences, each party wants to sendmen where the other party sends men if the platformpreference of the voters is favorable, or send men wherethe opponent sends women if the opposite is true. Thisleads to the following lemma:

Lemma 1. In any Nash equilibrium of the list compositiongame played at time 1 by the two parties, each party uses thesame mixed strategy in every district of the same region, andhence an equilibrium strategy of party p can be summarized

by the triplet (mjp).

Proof. Suppose instead that party S puts a man runningin district i with probability mS(i) < mS(i′), where i andi′ are in the same region j.

Then if j is a region in which L wins the man-manraces, the best response is to have mL(i′) > mL(i); butthis could not be compatible in equilibrium with thehypothesis, since the best response to the latter inequalityfor party S must have the feature mS(i) > mS(i′).

A similar contradiction arises if j is a region in which Swins the man-to-man races: in this case the best responseby L would have to satisfy mL(i) > mL(i′), but this in turncannot be compatible in equilibrium with the hypothesis,since the best response to the latter inequality by party Swould be mS(i) > mS (i′). �

The list composition game is, therefore, equivalentto a game where parties have to decide on proportions ofmen in each of the three regions. Suppose, for example,that z < � (the voters’ support of the L platform hasdecreased since the last election). Then parties have to

decide on m0zp , mz�

p , m�1p . The result is that a fraction m0z

L +(1 − m0z

L ) (1 − m0zS ) of L candidates are elected in region

[0, z), as all the men are elected, and, among the womenwho run (in proportion (1 − m0z

L )), all those who end uprunning against a woman also win the election, and theprobability of running against a woman is (1 − m0z

S ).Having explained the strategies for any probability

distribution over z, let us now choose a specific proba-bility distribution that will allow us to prove the result.Assume that z can take values in {0, 1 − �, �, 1}, withcorresponding probabilities equal to 0.5 − f , f , f , 0.5 −f , for some f ∈ (0.25, 0.5). (Thus f measures the skewnessof the distribution.)

Assume that b is infinitesimally small, so that it justi-fies a seat-maximizing behavior ceteris paribus but it canbe ignored in the computations. Given this assumption,the utility of party L is

UL =∫

i≤�

Ui di = � + a IL − CL if NL > 0.5

0.5� + aIL − CL if NL = 0.5

a IL − CL if NL < 0.5

and

US =∫

i≥�

Ui di = (1 − �) + a IS − CS if NS > 0.5

0.5(1 − �) + a IS − CS if NS = 0.5

a IS − CS if NS < 0.5.

Consider first the status quo (c = 0). At time 1, it isa dominant strategy for both parties to have only malecandidates. The expected utility is then

∀i ∈ [0, 1 − �) : U ei = a f + (1 + a) f

+ (0.5 − f )(1 + a)

= (0.5 + f )a + 0.5;

∀i ∈ [1 − �, �) : U ei = (1 + a) f + (0.5 − f )(1 + a)

= 0.5(1 + a);

∀i ∈ [�, 1] : U ei = (0.5 + f )a + 0.5.

Consider next the pure parity case (c = ∞). We firstanalyze the equilibrium of the list composition subgamesin the four possible cases, and then we deduce the expectedutility of each incumbent.

Case 1: z = 0; the 0.5 men candidates sent by S willbe elected, and necessarily at least some women will beelected too, so that S will win the election. It is optimalfor S to have all its incumbents running. Therefore, inregion [0, �], by lemma 1, the equilibrium strategies arem0�

L = 0.5�

and m0�S = �−0.5

�in every district of that region.

Consequently, each L incumbent has a probability 0.5�

ofrunning, and, if he runs, a probability 0.5

�of being elected.

All S incumbents are sure to be reelected.


Case 2: z = 1 − �. Sending all its 0.5 men to districtsin [1 − �, 1] guarantees 0.5 seats, and S is sure to havemore than that, so, again, S is sure to win the election.The equilibrium strategies are m0z

L = 1, mz�L = 1

2 , m�1L =

0 and m0zS = 0, mz�

S = 12 , m�1

S = 1. Incumbents in [0, z)and [�, 1] are sure to be reelected, whereas incumbents in[z, �) run with probability 1

2 and, if they run, are electedwith probability 1

2 .Cases 3 and 4: z = � or z = 1. L wins the election.

In this case party L tries to send men where S sendsmen, and S tries to send men where L sends women.Equilibrium strategies are m0�

L = 0.5�

, m�1L = 0 and m0�

S =�−0.5

�, m�1

S = 1. Incumbents from region [0, �) run withprobability 0.5

�and are sure to be reelected if they run.

The expected utilities computed at time 0 are asfollows:

∀i ∈ [0, 1 − �) : U ei = (0.5− f ) 0.52

�2 a + a f

+ 0.5

(1 + 0.5

�a

)

=(

0.52

�2 (� + 0.5− f )+ f)

a + 0.5;

∀i ∈ [1 − �, �) : U ei = (0.5− f ) 0.52

�2 a + 0.52a f

+ 0.5

(1 + 0.5

�a

)

= 0.52

�2 (� + 0.5 − (1−�2) f )a+0.5;

∀i ∈ [�, 1] : U ei = 0.5(1 + a) + 0.5a

= a + 0.5.

It is easy to see that S incumbents strictly prefer pureparity to no parity, as it guarantees their reelection.

Let us now consider the case of parity with fees (c =c∗ ∈ (0, ∞)). Take in particular any value of c∗ such that

Assumption a: a/2 > c∗ > b ≈ 0.Case 1: z = 0. At equilibrium, S must win the election.

Indeed, it has at least 0.5 seats (all its men are elected),and, if it is not sufficient to win, then it is worth paying thefee for one male candidate. So we can consider that S winsthe election with 0.5 men running. S tries to maximizethe number of seats obtained, so that the equilibriumwill be mixed, with M S (the number of men running forS in [0, �)) equal to � − 0.5. The utility of party L isUL = a 0.5

�ML − c∗(ML − 0.5) where M L stands for the

number of men running in [0, �). Rearranging, we getUL = ( 0.5

�a − c∗)ML + 0.5c∗, so that L pays the fees for

all its incumbents whenever 0.5�

a − c∗ > 0, that is, a >

2c∗ �, which holds given assumption a. Therefore, all theincumbents run, and 0.5 of them are elected. The averageutility among them is 0.5

�a − c∗(�−0.5)

�, whereas the utility

of each S incumbent is 1 + a.Case 2: z = 1 − �. As above, S is sure to win, provided

it runs all incumbents from � to 1 and the remaining

men (� − 0.5) randomly in the interval [z, �]. It hasno incentive to take a man from [�, 1] to [z, �), giventhat c∗ > b, nor to [0, z), as the probability for a manto be elected in that region is 0. If a man from party Lruns in [z, �], then his probability of being elected is 0.5.Utility of party L is U L = (1 − �)a + 0.5(M L − (� −0.5))a − c∗ (M L − 0.5). So party L will pay the fees, givenassumption a. For each incumbent in [0, 1 − �), Ui =a − c∗

�(� − 0.5), and the average utility of those from [1

− �, �) is 0.5a − c∗�

(� − 0.5). The utility of incumbentsof S is 1 + a.

Case 3: z = �. For a similar reason as above, L is sureto win. Party S sends all its incumbents, and sends menuniformly in [0, �). We have U L = 1 + aM L − c∗ (M L −0.5), so that M L = �, all to be reelected. The utility ofeach L incumbent is 1 + a − c∗

�(� − 0.5), and that of S

incumbents is a.Case 4: z = 1. The fact that L men are sure to be

elected even if they run in [�, 1] does not change thestrategy from the previous case, as paying the fee forhaving one more male candidate elected is not profitableif he is not an incumbent. The equilibrium utilities are,therefore, identical to what they are in case 3.

The expected utility of the incumbents can be com-puted as follows (letting C∗ stand for c∗

�(� − 0.5)):

∀i ∈ [0, 1 − �) : U ei = (0.5 − f )

(0.5

�a − C ∗

)

+ f(a − C ∗) + 0.5

(1 + a−C ∗)

=(

(0.5 − f )0.5

�+ f + 0.5

)a

+ 0.5 − C ∗;

∀i ∈ [1 − �, �) : U ei = (0.5 − f )

(0.5

�a − C ∗

)

+ f(0.5a − C ∗)

+ 0.5(1 + a − C ∗)

=(

(0.5 − f )0.5

�+ 0.5 f + 0.5

)a

+ 0.5 − C ∗;

∀i ∈ [�, 1] : U ei = 0.5(1 + a) + 0.5a

= a + 0.5.

At time 0: Let us now compare the expected utility of eachincumbent across the different possible values of c.

1) For incumbents in [0, 1 − �): it is clear that par-ity with fees is the system which maximizes theirprobability of being reelected. But the other con-sequence is that fees have to be paid. We havethat they prefer parity with fees to no parityiff a ≥ 2c∗ �−0.5

0.5− f , which can only be satisfied if0.5 − f is not too small. Let us note that a very


low 0.5 − f means that those incumbents are al-most sure to be reelected even without parity, sothat it is intuitive that no parity is the best systemfor them. Given our assumptions, it is sufficientto have 0.5 − f > � − 0.5, which is reasonable,in order to have the incumbents in this regionstrictly prefer parity with fees to no parity. Theyprefer pure parity to no parity iff 0.5 − f > 2�

(� − 0.5), which again means that the probabilityto be in a bad state is sufficiently large; but ob-serve that the threshold is more difficult to satisfythan in the previous case (it is more likely thatthose incumbents prefer parity with fees over noparity than them preferring pure parity over noparity). They prefer parity with fees to pure parityiff a ≥ 2�c∗(�−0.5)

�(�− f )−0.5(0.5− f ) , which is satisfied if thecondition above for parity with fees to dominateno parity holds. Thus, parity with fees is the bestfor those incumbents if 0.5 − f is sufficiently large.

2) For incumbents in [1 − �, �): parity with fees ispreferred to no parity iff a > 2c∗ �−0.5

0.5−(1−�) f . Butwe have already assumed that a > 2c∗, and thefraction is always lower than 1. Parity with fees ispreferred to strict parity iff a > 2c∗ �(�−0.5)

(1−�) f +�2+0.52 ,

and again the fraction is always smaller than 1.Consequently, parity with fees is always the strictlymost preferred solution in this region.

3) The incumbents in [�, 1] all strictly prefer a paritylaw, with whatever c > 0, to the status quo.

Consequently, given assumption a, there are many prob-ability distributions with many possible skewness levelssuch that parity with fees is strictly preferred by the ma-jority (the L incumbents) to any other system. Given thestrict preference by the S incumbents for any type of par-ity law over the status quo, the parity with fees reformcould win against the status quo even if the voting rulewere unanimity. �

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incumbents' interests and gender quotas

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